/[escript]/trunk/doc/examples/cookbook/example08b.py
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Annotation of /trunk/doc/examples/cookbook/example08b.py

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Revision 3892 - (hide annotations)
Tue Apr 10 08:57:23 2012 UTC (6 years, 10 months ago) by jfenwick
File MIME type: text/x-python
File size: 7656 byte(s)
Merged changes across from the attempt2 branch.
This version builds and passes python2 tests.
It also passes most python3 tests.



1 ahallam 3055
2     ########################################################
3     #
4     # Copyright (c) 2009-2010 by University of Queensland
5     # Earth Systems Science Computational Center (ESSCC)
6     # http://www.uq.edu.au/esscc
7     #
8     # Primary Business: Queensland, Australia
9     # Licensed under the Open Software License version 3.0
10     # http://www.opensource.org/licenses/osl-3.0.php
11     #
12     ########################################################
13    
14     __copyright__="""Copyright (c) 2009-2010 by University of Queensland
15     Earth Systems Science Computational Center (ESSCC)
16     http://www.uq.edu.au/esscc
17     Primary Business: Queensland, Australia"""
18     __license__="""Licensed under the Open Software License version 3.0
19     http://www.opensource.org/licenses/osl-3.0.php"""
20     __url__="https://launchpad.net/escript-finley"
21    
22     ############################################################FILE HEADER
23     # example08b.py
24     # Antony Hallam
25     # Seismic Wave Equation Simulation using acceleration solution.
26     # Extend the solution in example 08a to use absorbing boundary
27     # conditions.
28    
29     #######################################################EXTERNAL MODULES
30     from esys.escript import *
31     from esys.finley import Rectangle
32 caltinay 3346 from esys.weipa import saveVTK
33 ahallam 3055 import os
34     # smoothing operator
35     from esys.escript.pdetools import Projector, Locator
36     from esys.escript.unitsSI import *
37     import numpy as np
38 jfenwick 3148 import matplotlib
39     matplotlib.use('agg') #It's just here for automated testing
40    
41 ahallam 3055 import pylab as pl
42     import matplotlib.cm as cm
43     from esys.escript.linearPDEs import LinearPDE
44    
45 ahallam 3057 ########################################################MPI WORLD CHECK
46     if getMPISizeWorld() > 1:
47     import sys
48 jfenwick 3892 print("This example will not run in an MPI world.")
49 ahallam 3057 sys.exit(0)
50    
51 ahallam 3055 #################################################ESTABLISHING VARIABLES
52     # where to save output data
53     savepath = "data/example08b"
54     mkDir(savepath)
55     #Geometric and material property related variables.
56     mx = 1000. # model lenght
57     my = 1000. # model width
58 ahallam 3089 ndx = 300 # steps in x direction
59     ndy = 300 # steps in y direction
60 ahallam 3055 xstep=mx/ndx # calculate the size of delta x
61     ystep=abs(my/ndy) # calculate the size of delta y
62     lam=3.462e9 #lames constant
63     mu=3.462e9 #bulk modulus
64     rho=1154. #density
65     # Time related variables.
66 ahallam 3195 testing=True
67     if testing:
68 jfenwick 3892 print('The testing end time is currently selected. This severely limits the number of time iterations.')
69     print("Try changing testing to False for more iterations.")
70 ahallam 3195 tend=0.001
71     else:
72     tend=0.5 # end time
73    
74 ahallam 3089 h=0.0001 # time step
75 ahallam 3055 # data recording times
76     rtime=0.0 # first time to record
77     rtime_inc=tend/50.0 # time increment to record
78     #Check to make sure number of time steps is not too large.
79 jfenwick 3892 print("Time step size= ",h, "Expected number of outputs= ",tend/h)
80 ahallam 3055
81     U0=0.1 # amplitude of point source
82     ls=500 # length of the source
83     source=np.zeros(ls,'float') # source array
84     decay1=np.zeros(ls,'float') # decay curve one
85     decay2=np.zeros(ls,'float') # decay curve two
86     time=np.zeros(ls,'float') # time values
87     g=np.log(0.01)/ls
88    
89     dfeq=50 #Dominant Frequency
90     a = 2.0 * (np.pi * dfeq)**2.0
91     t0 = 5.0 / (2.0 * np.pi * dfeq)
92     srclength = 5. * t0
93 ahallam 3057 ls = int(srclength/h)
94 jfenwick 3892 print('source length',ls)
95 ahallam 3055 source=np.zeros(ls,'float') # source array
96     ampmax=0
97     for it in range(0,ls):
98     t = it*h
99     tt = t-t0
100     dum1 = np.exp(-a * tt * tt)
101     source[it] = -2. * a * tt * dum1
102     # source[it] = exp(-a * tt * tt) !gaussian
103     if (abs(source[it]) > ampmax):
104     ampmax = abs(source[it])
105     #source[t]=np.exp(g*t)*U0*np.sin(2.*np.pi*t/(0.75*ls))*(np.exp(-.1*g*t)-1)
106     #decay1[t]=np.exp(g*t)
107     #decay2[t]=(np.exp(-.1*g*t)-1)
108     time[t]=t*h
109     #tdecay=decay1*decay2*U0
110     #decay1=decay1*U0; decay2=decay2*U0
111     pl.clf();
112     pl.plot(source)
113     #pl.plot(time,decay1);pl.plot(time,decay2);
114     #pl.plot(time,tdecay)
115     pl.savefig(os.path.join(savepath,'source.png'))
116    
117     # will introduce a spherical source at middle left of bottom face
118     xc=[mx/2,0]
119    
120     ####################################################DOMAIN CONSTRUCTION
121 ahallam 3075 domain=Rectangle(l0=mx,l1=my,n0=ndx, n1=ndy,order=2) # create the domain
122 ahallam 3055 x=domain.getX() # get the locations of the nodes in the domani
123    
124     ##########################################################ESTABLISH PDE
125     mypde=LinearPDE(domain) # create pde
126     mypde.setSymmetryOn() # turn symmetry on
127     # turn lumping on for more efficient solving
128 ahallam 3405 mypde.getSolverOptions().setSolverMethod(mypde.getSolverOptions().HRZ_LUMPING)
129 ahallam 3055 kmat = kronecker(domain) # create the kronecker delta function of the domain
130     mypde.setValue(D=kmat*rho) #set the general form value D
131    
132     ##########################################################ESTABLISH ABC
133     # Define where the boundary decay will be applied.
134     bn=50.
135     bleft=xstep*bn; bright=mx-(xstep*bn); bbot=my-(ystep*bn)
136     # btop=ystep*bn # don't apply to force boundary!!!
137    
138     # locate these points in the domain
139     left=x[0]-bleft; right=x[0]-bright; bottom=x[1]-bbot
140    
141 ahallam 3057 tgamma=0.85 # decay value for exponential function
142 ahallam 3055 def calc_gamma(G,npts):
143     func=np.sqrt(abs(-1.*np.log(G)/(npts**2.)))
144     return func
145    
146     gleft = calc_gamma(tgamma,bleft)
147     gright = calc_gamma(tgamma,bleft)
148     gbottom= calc_gamma(tgamma,ystep*bn)
149    
150 jfenwick 3892 print('gamma', gleft,gright,gbottom)
151 ahallam 3055
152     # calculate decay functions
153     def abc_bfunc(gamma,loc,x,G):
154     func=exp(-1.*(gamma*abs(loc-x))**2.)
155     return func
156    
157     fleft=abc_bfunc(gleft,bleft,x[0],tgamma)
158     fright=abc_bfunc(gright,bright,x[0],tgamma)
159     fbottom=abc_bfunc(gbottom,bbot,x[1],tgamma)
160     # apply these functions only where relevant
161     abcleft=fleft*whereNegative(left)
162     abcright=fright*wherePositive(right)
163     abcbottom=fbottom*wherePositive(bottom)
164     # make sure the inside of the abc is value 1
165     abcleft=abcleft+whereZero(abcleft)
166     abcright=abcright+whereZero(abcright)
167     abcbottom=abcbottom+whereZero(abcbottom)
168     # multiply the conditions together to get a smooth result
169     abc=abcleft*abcright*abcbottom
170    
171     #visualise the boundary function
172 ahallam 3075 #abcT=abc.toListOfTuples()
173     #abcT=np.reshape(abcT,(ndx+1,ndy+1))
174     #pl.clf(); pl.imshow(abcT); pl.colorbar();
175     #pl.savefig(os.path.join(savepath,"abc.png"))
176 ahallam 3055
177    
178     ############################################FIRST TIME STEPS AND SOURCE
179     # define small radius around point xc
180 jfenwick 3892 src_length = 40; print("src_length = ",src_length)
181 ahallam 3055 # set initial values for first two time steps with source terms
182     y=source[0]*(cos(length(x-xc)*3.1415/src_length)+1)*whereNegative(length(x-xc)-src_length)
183 ahallam 3089 src_dir=numpy.array([0.,1.]) # defines direction of point source as down
184 ahallam 3055 y=y*src_dir
185     mypde.setValue(y=y) #set the source as a function on the boundary
186 ahallam 3405 # turn lumping on for more efficient solving
187     mypde.getSolverOptions().setSolverMethod(mypde.getSolverOptions().HRZ_LUMPING)
188 ahallam 3055 # for first two time steps
189 ahallam 3089 u=[0.0,0.0]*wherePositive(x)
190 ahallam 3055 u_m1=u
191    
192     ####################################################ITERATION VARIABLES
193     n=0 # iteration counter
194     t=0 # time counter
195     ##############################################################ITERATION
196     while t<tend:
197     # get current stress
198 ahallam 3089 g=grad(u); stress=lam*trace(g)*kmat+mu*(g+transpose(g))
199     mypde.setValue(X=-stress*abc) # set PDE values
200 ahallam 3055 accel = mypde.getSolution() #get PDE solution for accelleration
201     u_p1=(2.*u-u_m1)+h*h*accel #calculate displacement
202     u_p1=u_p1*abc # apply boundary conditions
203     u_m1=u; u=u_p1 # shift values by 1
204     # save current displacement, acceleration and pressure
205     if (t >= rtime):
206     saveVTK(os.path.join(savepath,"ex08b.%05d.vtu"%n),displacement=length(u),\
207     acceleration=length(accel),tensor=stress)
208     rtime=rtime+rtime_inc #increment data save time
209     # increment loop values
210     t=t+h; n=n+1
211     if (n < ls):
212     y=source[n]*(cos(length(x-xc)*3.1415/src_length)+1)*whereNegative(length(x-xc)-src_length)
213     y=y*src_dir; mypde.setValue(y=y) #set the source as a function on the boundary
214 jfenwick 3892 print(n,"-th time step t ",t)

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